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Faculty workgroups offer a chance to reflect on teaching practices and course design
I tuned in last night to live early coverage of the Iowa caucuses. The commentators made it seem demographically unfeasible for Bernie to pull off an upset, yet this morning he was crowing about a virtual tie. His optimistic take on the outcome had to be forced out of the media, who preferred to lead their news bulletin with the more definitive headline "Clinton and Cruz win in Iowa".
The weather report said temperatures would dip almost to freezing before sunrise. Since I had to leave the house when it was still dark and I didn't want to take the risk of a bike crash before meeting two of my classes for the first time, I decided to make the commute on foot. The sidewalks still felt slippery in some places, but I managed not to fall and still arrived on campus by 7:15, a nickel richer than I would have been if I hadn't walked.
I grabbed the folder of MATH 080 goal sheets from my MP office and brought them to the SS building, where I would teach and hold office hours until 11:00. Until the semester picks up and more students become aware of my office hours, the 9:30-11 time slot on Tuesdays will serve as the perfect time to get caught up on individual emails to MATH 080 students informing them of this week's goals. Today I just managed to send off the last of 26 individual emals by the end of my 90 minutes in the office.
Setting up for the first meteorology class involved gathering supplies from SS325A and SS120 for the demo on Sun-Earth interactions. I already had enough copies of the syllabus and the syllabus quiz thanks to a copying job in MP248 just before yesterday's evening class. The syllabus quiz proved itself more conducive to student engagement and peer-to-peer interaction than incorporating syllabus key points into my lecture, and it actually resulted in students reading more of the syllabus than just the sections needed to answer the quiz questions. I devoted only a few sentences to explaining the ePortfolio requirement, much less than it appeared Kim Fouche spent in her MATH 130 class. The majority of the class period was taken up by the PowerPoint presentation on Sun-Earth relationships, with two pauses for students to summarize some key ideas in their own words. In the closing minutes I pulled up the Blackboard course site and showed the details of Inquiry 1.
In my MATH 080 class, the recent delivery of personalized student emails helped ensure that everyone was starting on the correct lesson, even though the past due status of lesson 1.2 had been cleared for the entire class. Students whose first sign-in took place in the classroom (rather than at home as we had hoped would happen during the week of snow closures) were placed at the right starting point with the assistance of Professor Hill working from the back row.
A packed classroom made it difficult to navigate the rows and have individual consultations with everyone. Insufficient time was also a factor, since the welcome presentation took up fully half an hour. Next week I should be able to sit down with every student personally and talk about short-term goals, even if we start with a five-minute icebreaker or warm-up exercise.
Notes from the SBG Meeting
More voluble contributions came from Jack today, on the topics of hyperbolic functions, examples from engineering, and student algebra weaknesses. Steve made interesting points on the possibility of splitting the precalculus curriculum into two semesters, allowing for the more leisurely exploration of analytic geometry and vector algebra in the second semester.
When explaining Standards Based Grading to outsiders, we should try to separate benefits to the student from benefits to the instructor. Students don't need to see all the reasons we're adopting the practice, only the reasons that are intelligible to them.
Guiding principles when culling the list of standards:
1. Eliminate overlap. If similarly worded standards emerge from our reading of different sections, either delete all but one of them or make them all narrower with additional qualifiers.
2. Each standard should be objectively assessable. Vague language referring to "understanding" should be replaced by less subjective measures.
Who benefits from splitting the precalculus curriculum into two semesters?
Who suffers from splitting the precalculus curriculum into two semesters?
Recertification of all 100-level math courses is underway at Montgomery College this semester. This process is intended to ensure that the general education objectives inform the design of any course that might be taken to satisfy distribution requirements. The use of standards-based-grading (SBG), in which assessments are narrowly focused on individual skills throughout the semester, might seem antagonistic to the goal of students' following a broad "thematic pathway" during their time in our institution. In response to a concern shared by the leader of our SBG study group (that a GenEd course could not simultaneously be a SBG course), I spoke with some other MATH 181 instructors on my campus and came up with the following points.
The perceived incompatibility between a course's GenEd designation and grading by standards is probably exaggerated, even though I alluded to as much in reason #2, bullet point 3, of the "Top Reasons for SBG" document. ("SBG confers a more standardized meaning on your final grade in the course. ..., [a reason which] applies mainly to courses that have a direct sequel within the same department, since the various majors that feed students into a "service course" often have different interpretations of what the essential learning outcomes are.")
In my mind, the use of SBG to ensure transferrability of course credits is a vital safeguard against the common practice of 4-year institutions such as UMCP forcing our graduates to repeat content that they've already mastered. This role can still be played by SBG, if all instructors of the course agree to input the final grades as determined by the standards-based calculation. When the schools reviewing transfer applicants see that our final grades are standards-based, their insistence on repeating a course "to protect the integrity of their major" becomes less defensible.
What GenEd recertification asks us to do is complementary to this goal of transferrability. With SBG we're allowing students to take ownership of their learning, but only within the bounds set by the course objectives. The signature assignments allow students to take their ownership of the learning process beyond those course boundaries, integrating their life experiences, their other coursework, and their mathematical skills to create work that reflects their individual talents and interests. Such signature assignments force them to answer for themselves the question "when am I ever going to use this?" By answering that question with a personalized capstone project, students become capable of marketing themselves to constituencies external to academia.
In short, as Sean Cornally put it in his Think Thank Thunk blog, SBG is a gateway drug that sets instructors down the path of creating a student-centered learning environment. GenEd recertification, with its focus on integrative learning opportunities, continues down that path and gives students even more freedom in crafting representative samples of their work. We as instructors don't have to give those signature assignments any weight in the final grade, using only SBG for that purpose so that transferrability of credits is ensured. The self-promotion potential that signature assignments provide will be reason enough for our students to engage with them whole-heartedly, as I'm seeing with my MATH 110 students in their ePortfolios.
Recent essays and cognitive science studies have documented the effect on our thinking of the many hours we spend each day staring at computer screens. Attention spans appear to have decreased, and our productivity might even have plateaued after decades of strong gains. Sophie McBain's recent essay in New Statesman looks specifically at the changes in our memory. Here is the outline for an essay that connects that article to fields beyond cognitive science.
1. Uploading our memories to a cloud of networked computers changes the way we perceive our life experiences.
2. Jordan Ellenberg, in How Not to Be Wrong, likens mathematics to a prosthetic limb, engineered to have more lifting power than the human muscles endowed by our genetic heritage.
3. Questions
Yesterday I answered the call to cover Lori Christy's opening shift in P1-101A, which put me on the road to campus this morning several hours before I'm normally out the door on Fridays. I dropped off a few things in the part-time faculty office before calling security to get the door of 101A opened.
Because Fridays normally see a lot of traffic from MATH 080 students, there were two student assistants in the open classroom that first hour, wandering the aisles and responding to raised hands that signal needed help. The testing row filled up rather quickly, but still by 9:45 there was one seat available when another student showed up to take a test.
Kim Fouche appeared at the very beginning to explain the presence of a student of hers who would be working from a printed textbook rather than the computer, and to lament the loss of Lori for the day, whose experience might have helped settle an issue regarding testing at DSS. From these opening minutes until Skip Mahaney walked in at 10:00, I was the only faculty member in the room, but the students' need for my administrative services was actually quite manageable.
Leaving the open classroom at 10:00, I could have returned to the part-time faculty office and set up camp for the rest of the day until my MATH 110 problem solving session, but I was tempted by the idling MC shuttle to partake in a change of scenery and spend the mid-day hours at Rockville. Acquiring a set of AMS pressure blocks for my meteorology students to play with next week would serve as one motivation for the trip. Also in Rockville I might have been able to share a Skype connection with one of the other faculty members on the SBG group, in the event that installing Skype on my laptop and configuring the microphone proved too troublesome. A third reason for the mid-day excursion was to put some distance between me and the easy food options of downtown Silver Spring, so that the weekly total spent on food would not balloon into the $40 range so early in the year. Unfortunately this plan also barred me from walking home for lunch, leaving me to face the 14:00 Skype conference call with very low blood sugar and too many hours of sedentary work.
Thesis Statements of Various Interlocutors in Recent Weeks
Thomas Frank, in Listen, Liberal:
The Democratic Party has ceased to represent the interests of working-class Americans and has ingratiated itself instead to the so-called creative classes of Silicon Valley and Wall Street. By framing the public debate about wealth disparities in terms of innovation and increased access to education, the party ignores the role played by power relations and the loss of union representation for the working class.
Mike Lofgren, in The Deep State:
Electoral politics might as well be a spectator sport for all the good it does to change the arc of American business and military affairs. No matter who is nominally at the head of government, the set of acceptable actions has been constrained by interest groups, from Wall Street and Silicon Valley to DOD contractors, before an elected president even takes office.
Max Frisch, in The Firebugs:
Any of us can be tricked into allowing unwholesome influences to take root in our lives. We fear so much the possibility of being disliked that we entertain dangerous guests and believe dangerous ideas, allowing them to linger and become for us the new normal.
Mazen Zarrouk, at 10 a.m.:
After three meetings of the precalculus curriculum revision workgroup, no firm recommendations have been set for fall semester implementation. Gateway exams and more modular lessons have come up in discussion, making the course more like MATH 080 in its delivery. The instructor should still be given the chance to provide the big picture to students, so the course can't be entirely self-paced.
Brian Mastro, at 10:30 a.m.:
Striking Verizon workers demonstrate that organized labor still can assert power over large corporations. Even in healthcare delivery it should be possible to unionize nurses and doctors, wresting power back from the big hospitals and insurance companies.
Kim Fouche, at 11 a.m.:
When teaching MATH 080 you expect to have students from the lower end of the math ability distribution. It can be frustrating to find students from those same ability levels filling the MATH 130 classroom, since you know their math phobia has a good chance of being passed down to the kids in their elementary school classes.
James Lang, in the Chronicle of Higher Education:
(March 7) A more productive use of the last five minutes of class is to practice metacognition. Don't try to cram in new ideas or grand syntheses that won't be appreciated (in one ear and out the other). Have students test their recollection of the key points, and celebrate whatever level of understanding they do manage to demonstrate.
(April 3) Give students some freedom in designing the course -- what to focus on and how to assess. Maybe a blank spot on the syllabus that can be filled in using student input after several weeks have gone by.
Carol Moore, in the Micro-Interventions workshop:
Can any of the coaching practices needed for MATH 080 be adapted to serve students in the higher-level math classes?
A rubric based on Bloom's taxonomy can help avoid assessing students on higher-level skills before they've had a chance to practice them. (cf. Ellen Olmstead's moving window through which she views her students' essays as the semester progresses.)
Brad Stewart, in the Micro-Interventions workshop:
How high up the ladder of math courses can the practice of mastery-based learning be deployed? At Virginia Tech even the calculus courses are taught using modular computer lessons.
Regarding a proposed implementation of standards-based grading
As suggested by Jojo last Monday, our summer pilot study of SBG might assess each standard as follows:
We would count anything that's 2 or 3 as mastery, but for the "A" and "B", we would use the 3 scores to distinguish them from the the "C" students.
I would support using this version for courses such as MATH 181, where D and F have the same implications for enrolling in the sequel. In a standalone course like MATH 110, I would use a 5 point scale (0,1,2,3,4) so that college credit might still be earned for "D-level" work. While some four-year institutions might not grant college credit for a D in MATH 110, at least the public universities in this state are required to transfer all credits in a lump sum if the applicant has earned an associate's degree.
One might visualize a student's demonstration of mastery by plotting a step function, with standards as unit intervals on the x-axis and the scores for each standard represented by the height of a bar. Since this pilot study is taking place in a calculus course, why not specify the thresholds for each letter grade using integrals of such a step function f? For instance, find the integral of fx[core]+0.5fx[non-core] where x[S] is the indicator function for set S. Possible thresholds for the various grades would then be almost identical to the usual mapping between numbers and letters.
On a slightly different topic, one of the challenges I faced this semester had to do with shoehorning the reflective learning component into the SBG grading scheme that I tried out in MATH 110. I designed three prompts loosely based on the standards I wanted to assess, and hoped that my students' reflections could be mapped onto these standards. When the submissions came in, I had trouble reconciling my desire to incentivize creative exploration with the SBG mantra of counting only the best instance of a skill being demonstrated. In the case of my math students, counting the best instance of an assessed standard would result in their homework grades overwriting even the most disappointing ePortfolio reflection.
This realization highlights the difficulty of using multiple assessment types in an SBG classroom. On the one hand, we want to make sure our students are comfortable expressing their knowledge in a variety of situations, not just on their strongest type of assessment. On the other hand, SBG asks us to meet the student where they're at, giving greater weight to the assessment where they've done the best.
In a calculus class it's not too difficult to incentivize homework completion, since at this point in their college careers the students are aware that they can't learn passively any more. Hence SBG can be implemented using only one type of assessment (in-class quizzes or tests). In classes that rely on two or more assessment types, however, the end-of-semester gradebook reconciliation can be a daunting exercise in reevaluating priorities.